What is the time period for which Rs. 8000 amounts to Rs. 12000 at 2% p.a. of simple interest ?

Options

A. 4 years
B. 2.5 years
C. 3.25 years
D. 6 years

Answer

To solve the problem of finding the time period for which Rs. 8000 amounts to Rs. 12000 at a simple interest rate of 2% per annum, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Principal (P) = Rs. 8000
- Amount (A) = Rs. 12000
- Rate (R) = 2% per annum

2. **Calculate the Simple Interest (SI):**
- Simple Interest (SI) can be calculated using the formula:
\[ SI = A - P \]
- Substituting the values:
\[ SI = 12000 - 8000 = 4000 \]

3. **Use the Simple Interest Formula:**
- The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
- We need to find the time period (T), so we rearrange the formula to solve for T:
\[ T = \frac{SI \times 100}{P \times R} \]

4. **Substitute the Known Values into the Formula:**
- Now, substituting the values we have:
\[ T = \frac{4000 \times 100}{8000 \times 2} \]

5. **Simplify the Expression:**
- First, calculate the denominator:
\[ 8000 \times 2 = 16000 \]
- Now substitute this back into the equation:
\[ T = \frac{400000}{16000} \]

6. **Perform the Division:**
- Simplifying the fraction:
\[ T = 25 \]

7. **Conclusion:**
- The time period for which Rs. 8000 amounts to Rs. 12000 at 2% per annum of simple interest is **25 years**.